The pair are considered two of Brazil's most exciting young talents and both have already been capped by the Selecao.
Barca considered making a move for Damiao last summer and remain interested in acquiring the services of an out-and-out centre forward to add an extra dimension to their attack, according to Sport.
The striker was heavily linked with a transfer to Tottenham Hotspur during last month's transfer window and his agent, Vinicius Prates, recently hinted that his client's days with Internacional are numbered.
"In January, the club and the player decided to focus on the Copa Libertadores, but in July the situation can change," he revealed.
Sport also claims that Barca mulled over a bid for Oscar before the start of the current campaign, with the intention of first blooding him in the B team before gradually introducing him to the senior squad.
The Catalans have reportedly been closely monitoring the progress of a midfielder that first caught their eye when he was playing in a Nike Cup in England when he was just 15.
Since November, Goal.com has been publishing exclusive extracts from Graham Hunter's highly-anticipated new book, 'Barca: The Making of the Greatest Team in the World'. The very last extract, which was published on Friday, looks at Andres Iniesta's risky return from injury in the 2009 Champions League Final and how he was described by Wayne Rooney as the 'best midfielder in the world'. Don't miss it!